Parabola
 |  |  |  | |
| Equation | y^2 = 4ax | y^2 = -4ax | x^2 = 4ay | x^2 = -4ay |
| Coordinates of Focus | (a, 0) | (-a, 0) | (0, a) | (0, -a) |
| Coordinates of Vertex | (0, 0) | (0, 0) | (0, 0) | (0, 0) |
| Equation of Axis of Symmetry | y = 0 i.e. X Axis | y = 0 i.e. X Axis | x = 0 i.e. Y Axis | x = 0 i.e. Y Axis |
| Length of Latus Rectum | 4a | 4a | 4a | 4a |
| Equation of Directrix | x = -a | x = a | y = -a | y = a |
Ellipse
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| Equation | \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 a>b | \frac{x^2}{b^2} + \frac{y^2}{a^2} = 1 a>b |
| Coordinates of Focus | (\pm c, 0) | (0, \pm c) |
| Coordinates of Vertex | (\pm a, 0) | (0, \pm a) |
| Relation between a, b and c | a^2 = b^2 + c^2 | a^2 = b^2 + c^2 |
| Equation of Major Axis | y = 0 i.e. X Axis | x = 0 i.e. Y Axis |
| Length of Major Axis | 2a | 2a |
| Equation of Minor Axis | x = 0 i.e. Y Axis | y = 0 i.e. X Axis |
| Length of Minor Axis | 2b | 2b |
| Length of Latus Rectum | \frac{2b^2}{a} | \frac{2b^2}{a} |
| Equation of Directrix | x = \pm \frac{a}{e} | y = \pm \frac{a}{e} |
Hyperbola
 |  | |
| Equation | \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 | \frac{y^2}{a^2} - \frac{x^2}{b^2} = 1 |
| Coordinates of Focus | (\pm c, 0) | (0, \pm c) |
| Coordinates of Vertex | (\pm a, 0) | (0, \pm a) |
| Relation between a, b and c | c^2 = a^2 + b^2 | c^2 = a^2 + b^2 |
| Equation of Transverse Axis | y = 0 i.e. X Axis | x = 0 i.e. Y Axis |
| Length of Transverse Axis | 2a | 2a |
| Equation of Conjugate Axis | x = 0 i.e. Y Axis | y = 0 i.e. X Axis |
| Length of Conjugate Axis | 2b | 2b |
| Length of Latus Rectum | \frac{2b^2}{a} | \frac{2b^2}{a} |
| Equation of Directrix | x = \pm \frac{a}{e} | y = \pm \frac{a}{e} |